Survey Proportion Margin of Error Calculator

Method and input definitions

Margin = z × √(p(1 − p) ÷ n). If a finite population N is supplied, multiply by √((N − n) ÷ (N − 1)). z values used are 1.645, 1.96, and 2.576 for 90%, 95%, and 99%.

Worked example

For n = 400, p = 0.50, 95% confidence, and no finite-population correction, margin = 1.96 × √(0.25 ÷ 400) = 0.049, or 4.90 percentage points.

Assumptions and limits

This is the Wald normal approximation for a proportion under a simple random sample; it can be inaccurate for small samples or proportions near 0/1 and excludes nonresponse, design effects, and measurement error. NIST §7.2.4.1 presents exact binomial-tail limits; this page uses that as a contrast, not as the source of the Wald formula.

Inputs are bounded to finite values shown in the form. Displayed results are rounded for readability (probability percentages and proportion fractions to four, other measures to two decimal places); whole-count outputs remain exact. A changed field clears a prior result so an outdated estimate is not presented as current.

References and related tools

NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.4.1: Confidence Limits for the Binomial Distribution . NIST presents exact binomial-tail limits; this calculator instead shows the separately stated Wald normal approximation.

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